Question

The CP of $21$ articles is equal to SP of $18$ articles. Find the gain or loss
percent.
A. $16\dfrac{2}{3}\% $
B. $8\% $
C. $10\% $
D. $12\% $

Answer 1

Hint: Use $\begin{array}{l}
Gain\% = \dfrac{{Gain \times 100}}{{C.P.}}\\
Loss\% = \dfrac{{Loss \times 100}}{{C.P.}}
\end{array}$
For Gain, Selling Price should be greater than Cost price,
Whereas,
For loss, selling price is less than Cost Price.

Complete step-by-step answer:
Given that: The Cost Price C.P. of $21$ articles is equal to the Selling Price S.P. of $18$
articles.
Let Cost Price of an article be = $1$ Rupee
Therefore, Cost Price of $21$ articles $ = 21$
Selling Price of $18$ articles = $21$
Therefore, Selling Price of $1$ article $ = \dfrac{{21}}{{18}}$
Therefore, Selling Price is greater than cost Price.
S.P. > C.P.
Since,
$\dfrac{{21}}{{18}} > 1$
Therefore, It is gain.
Gain= S.P. – C.P.
$\begin{array}{l}
= \dfrac{{21}}{{18}} - 1\\

= \dfrac{{21 - 18}}{{18}}
\end{array}$

Gain=$ \dfrac{{3}}{{18}}$

Hence, $Gain\% = \dfrac{{Gain \times 100}}{{C.P.}}$
$\begin{array}{l}
Gain\% = \dfrac{3}{{18}} \times 100\\
Gain\% = 16.67\\

\end{array}$
Converting the decimal points in the fraction form-
$Gain\% = 16\dfrac{2}{3}\% $
This is the required answer and $Gain\% = 16\dfrac{2}{3}\% $
Therefore, option A is correct.

Additional Information: Generally, Profit and loss are used in finance and business
transactions to check whether the business has made a profit or loss during a particular period
of account. Certainly it can be done by deducting all the expenditure from total income the
profit or loss of the business.

Note: Always start this type of problems assuming respective variable x or any value such as
1,10,100 and fetch the relation between the selling price or the cost price which is greater or
smaller comparatively.